description-logic

Translate english sentences to ALC description logic

I have the following two English sentences:

  1. Mary is a Person.
  2. Bulldog is a specie of dog. French bulldog is a specie of bulldog.
  3. The only kind of dog that Mary owns is French bulldog.

I would like to know which of the following ways is the correct way to translate the third and the sentences based on the knowledge given.

1st approach

Bulldog ⊆ Dog 
FrenchBulldog ⊆ Bulldog
FrenchBulldog ⊆ Dog

(∀owns.FrenchBulldog ⨅ Person)(MARY)

2nd approach

∀owns.Bulldog ⊆ ∀owns.Dog 
∀owns.FrenchBulldog ⊆ ∀owns.Bulldog

(¬(∀owns.Dog⊔Bulldog) ⨅ ∀owns.FrenchBulldog ⨅ Person)(MARY) (*)

3rd approach

Bulldog ⊆ Dog 
FrenchBulldog ⊆ Bulldog

(Person⨅(∀owns.FrenchBulldog⨅(∀owns.¬Dog⊔∀owns.¬Bulldog)))(MARY) (**)

I know that the first approach is correct. But I would like to re-written the third English sentence as approaches 2-(*), 3-(**).

Thanks in advance for any advice.

Solution

  • Your approach 1 is correct and approaches 2 and 3 are incorrect.

    I assume with

    (¬(∀owns.(Dog⊔Bulldog)) ⨅ ∀owns.FrenchBulldog ⨅ Person)(MARY)

    by adding (¬(∀owns.(Dog⊔Bulldog)) you trying to ensure Mary only owns FrenchBulldogs, but it is achieving the opposite.

    (¬(∀owns.(Dog⊔Bulldog)) ≡ ∃owns.¬(Dog⊔Bulldog) ≡ ∃owns.(¬Dog ⨅ ¬Bulldog)

    Thus in essence you are saying that Mary owns only French bulldogs (∀owns.FrenchBulldog) AND you are saying she owns at least 1 thing that is not a dog and not a bulldog (∃owns.(¬Dog ⨅ ¬Bulldog)).